Space-harmonic analysis of periodically supported beams: response to convected random loading

Abstract The solution for the response of stiffened beams due to a spatial and temporal harmonic pressure has been obtained in the form of a particular series of space harmonics, evolved from considerations of progressive wave propagation. The superiority of this method over the classical normal mode approach is indicated. It is applied to obtain the r.m.s. curvature at a point on a periodically supported beam excited by a random acoustic plane wave or boundary layer pressure fluctuation. The results obtained with different numbers of terms in the series are compared with known closed-form solutions. When seven terms are included, results bear good agreement with the exact solution and as few as three terms yield a solution of acceptable accuracy. The method of space harmonics can be adapted to the case of orthogonally stiffened plates which are excited by pressure fields convected across the plates at oblique angles to the direction of stiffeners. The general method should be applicable to the estimation of response of orthogonally stiffened cylindrical structures.